hazelnut01 wrote:If k is a positive Integer, how many unique Prime Factors Does 14k have ?
(1) k^4 is divisible by 100
(2) 50*k has 2 Prime Factors
OA=C
First, REPHRASE the question:
We know how many unique prime factors 14 has: two (2 and 7). It would not be enough to know how many unique prime factors k has, since k may also contain factors of 2 or 7. These wouldn't be unique.
Target question: how many prime factors other than 2 or 7 does k have?
(1) k^4 is divisible by 100
Knowing one thing that a number is divisible by gives us only partial information. We know that it contains at least a 2 and a 5, but we don't know what else it may or may not be divisible by.
(2) 50*k has 2 Prime Factors
As GMATinsight points out, this tell us that k has no factors *other than* 2 and 5, but it could contain both, only one of the two, or neither (if k = 1). This doesn't give us enough to answer the question:
- if k contains 2 and 5, 14k will have 3 unique factors: 2,5, 7
- if k contains a 5 only, 14k will have 3 unique factors: 2,5, 7
- if k contains a 2 only, 14k will have 2 unique factors: 2,7
- if k contains neither (k = 1), 14k will have 2 unique factors: 2,7
Together:
k must contain a 2 and a 5 (per stmt 1), but if does not contain any other factors (per stmt 2). Therefore, 14k must contain unique factors of only 2, 5, and 7. Sufficient.
What is the source of this question?
You must always post your sources - it is a copyright violation not to do so.Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
